论文标题
渐近单极模量空间的同源稳定性
Homology stability for asymptotic monopole moduli spaces
论文作者
论文摘要
我们证明了两种不同风味的渐近单极模量空间的同源稳定性，即框架单极框的模量空间和理想单极的模量空间。前者是长臂猿 - 曼顿圆环捆绑包上的配置空间，而后者则是通过用骨构建用单极模量空间代替光纤的每个圆因子来获得的。它们在经典单极模量空间的部分压实中形成边界超曲面。我们的结果取决于配备有非本地数据的配置空间的一般同源稳定性结果。
We prove homological stability for two different flavours of asymptotic monopole moduli spaces, namely moduli spaces of framed Dirac monopoles and moduli spaces of ideal monopoles. The former are Gibbons-Manton torus bundles over configuration spaces whereas the latter are obtained from them by replacing each circle factor of the fibre with a monopole moduli space by the Borel construction. They form boundary hypersurfaces in a partial compactification of the classical monopole moduli spaces. Our results follow from a general homological stability result for configuration spaces equipped with non-local data.
